At What Height Is a Projectile at Half Its Initial Velocity?

[DaMastaofFisix]

Hello, I am practicing for the INternational Physics Olympiad qualifier and I was working on a practice test when I stumbles across what seemed like an easy problem. I thought It was super-intuitive, but I can't seem to verify a correct answer with the multiple choice selection. Here's the Problem:

A ball ( or projectile, no matter) is thrown vertically with a velocity V. The ball reaches a maximum height h. In terms of h, at what height is the ball traveling at half of its initial velocity?

Seemed easy at first, cause I knew and still know that it's a matter of plugging into the kinematics equations. the problem is that my logical setup isn't working out. I tried using the formula V^2=V0^2-2gh, but uh... it's not workin out Can someone come to my rescue!?

 

[Doc Al]

What's the problem? First figure out what h is in terms of V. Then try using that formula to find the new height.

 

[verty]

The only hint I can give is to write formulas for h and h_2 and then get h_2 in terms of h.

 

[daniel_i_l]

In your equation V^2=V0^2-2gh the h that comes out is the height when the ball gets to half oh the velocity (if V = 0.5 V0), with tht you can also find the total height, the just divide the middle-speed height with the final height and find how they are related. For example if Hm = 3 and Hf = 4 then Hm/Hf = 3/4 so Hm = 3/4Hf